On Steenrod L-homology, generalized manifolds, and surgery

Friedrich Hegenbarth (Avtor), Dušan Repovš (Avtor)

Povzetek

The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized ▫$n$▫-manifold ▫$X^n$▫, in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the ▫$n$▫th Steenrod homology group ▫$H^{st}_n (X^n, \mathbb{L}^+)$▫, where ▫$\mathbb{L}^+$▫ is the connected covering spectrum of the periodic surgery spectrum ▫$\mathbb{L}$▫, avoiding the use of the geometric splitting procedure, the use of which is standard in surgery on topological manifolds.

Ključne besede

Poincaré duality complex;generalized manifold;Steenrod ▫$\mathbb{L}$▫-homology;periodic surgery spectrum ▫$\mathbb{L}$▫;fundamental complex;$\mathbb{L}$-homology class;Quinn index;

Podatki

Jezik:	Angleški jezik
Leto izida:	2020
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	515.14
COBISS:	18947417
ISSN:	0013-0915
Št. ogledov:	465
Št. prenosov:	242
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 579-607
Letnik:	ǂVol. ǂ63
Zvezek:	ǂno. ǂ2
Čas izdaje:	May 2020
DOI:	10.1017/S0013091520000012
ID:	11758057